# Mathematical method for calculating batch fragmentations and their impacts on product recall within a FIFO assignment policy

## TL;DR

This paper introduces a mathematical approach to quantify batch fragmentation and its influence on product recalls under FIFO policies, enabling proactive recall strategies through a new fragmentation indicator and probabilistic analysis.

## Contribution

It presents a novel mathematical method and a management indicator to assess batch fragmentation impact on recalls, integrating proactive recall planning into batch sizing decisions.

## Key findings

- Fragmentation amplifies recall impact during crises.
- New equation accurately predicts expected recall size.
- Simulation confirms effectiveness of the proposed approach.

## Abstract

This study explores the interactions between order sizes, batch sizes and potential product recalls within a FIFO assignment policy. Evidence is provided that the extent of a product recall is related to the fragmentation of the batches of input materials as it amplifies the impact of a crisis. A new management indicator is proposed in order to quantify the expected number of fragments composing a customer order FrBO. A probabilistic analysis reveals that for a given likelihood of crisis, the presence of different batches in a customer order will largely increase its risk. Accordingly, a new equation is proposed for calculating the expected recall size. Taking into account the fragmentation measure allows, for the first time, for the integration of a proactive product recall policy in the batch sizing decision process. A Monte Carlo simulation is performed to validate the effectiveness of this approach.

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Source: https://tomesphere.com/paper/1905.08651